Name: PHYS122 Hourly Exam 3 1. The long, straight wire shown in Figure 1 above is in the plane of the page and carries a current I. Point P is also in the plane of the page and is a perpendicular distance d from the wire. Gravitational effects are negligible. (a) What is the direction of the magnetic field at point P due to the current in the wire? A particle of mass m and positive charge q is initially moving parallel to the wire with speed v0 when it is at point P, as shown in the figure below. (b) What is the direction of the magnetic force acting on the particle at point P? (c) Determine the magnitude of the magnetic force acting on the particle at point P in terms of the given quantities and fundamental constants. d I •d m, q I v0PHYS122 Exam 3 -2- (d) An electric field is applied that causes the net force on the particle to be zero at point P. i. What is the direction of the electric field at point P that could accomplish this? ii. Determine the magnitude of the electric field in terms of the given quantities and fundamental constants.PHYS122 Exam 3 -3- 2. A particle of mass m and charge q is accelerated from rest in the plane of the page through a potential difference ∆V between two parallel plates as shown above. The particle is injected through a hole in the right-hand plate into a region of space con-taining a uniform magnetic field of magnitude B oriented perpendicular to the plane of the page. The particle curves in a semicircular path and strikes a detector. (a) i. State whether the sign of the charge is positive or negative. ii. State whether the direction of the magnetic field is into the page or out of the page. (b) Determine each of the following in terms of m, q, ∆V, and B. i. The speed of the charged particle as it enters the region of the magnetic field B Region of Magnetic Field B ∆V Hole Detector q mPHYS122 Exam 3 -4- ii. The force exerted on the charged particle by the magnetic field B iii. The distance from the point of injection to the detector iv. The work done by the magnetic field on the charged particle during the se-micircular trip.PHYS122 Exam 3 -5- 3. A force F is applied to a conducting rod so that the rod slides with constant speed v over a frictionless pair of parallel conducting rails that are separated by a dis-tance l. The rod and rails have negligible resistance, but the rails are connected by a resistance R, as shown above. There is a uniform magnetic field B perpendi-cular to and directed out of the paper. (a) On the following diagram, indicate the direction of the induced current in the resistor. Determine the following in terms of v, B, l, and R. (b) The induced emf in the rod (c) The electric field in the rod l R vF B (out of paper) RailsRodPHYS122 Exam 3 -6- (d) The magnitude of the induced current in the resistor R (e) The power dissipated in the resistor as the rod moves in the magnetic field (f) The magnitude of the external force F applied to the rod to keep it moving with constant speed vPHYS122 Exam 3 -7- Equations 122EKqqFr= 29201Nm8.99 104CKπε==×271.67 10 kgpm−=× on qFEq→=r 2014qErπε= 0QEAε= 191.6 10 Ce−=× 319.11 10 kgem−=× 21202C8.85 10Nmε−=× EUqV= 12 12014Eqq qqUKrrπε== 014qqVKrrπε== VEdΔ= QCV=Δ 0ACdκε= ()221122CQUCVC==Δ QItΔ=Δ VIRΔ= LRAρ= WPIVt==Δ in outII=∑∑ loop0iiVVΔ=Δ=∑ 12sNRRR R=+++K 12pNCCC C=+++K 12111 1pNRRR R=+++K 12111 1sNCCC C=+++K 70Tm410Aμπ−=× 0wire2IBrμπ= 0loop2NIBRμ= solenoid 0NBILμ= sinBFqvBθ= wireFILB= cosBABθΦ= emfBBLvtΔΦ==Δ
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